Testing for preferred-frame effects in gravity with artificial Earth satellites.

As gravity is a long-range force, one might $a$ priori expect the Universe's global matter distribution to select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, two parameters suffice to describe the phenomenology of preferred-frame effects. One of them has already been very tightly constrained ($|{\ensuremath{\alpha}}_{2}|l4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, 90% C.L.), but the present bound on the other one is much weaker ($|{\ensuremath{\alpha}}_{1}|l5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, 90% C.L.). It is pointed out that the observation of particular orbits of artificial Earth satellites has the potential of improving the ${\ensuremath{\alpha}}_{1}$ limits by a couple of orders of magnitude, thanks to the appearance of small divisors which enhance the corresponding preferred-frame effects. There is a discrete set of inclinations which lead to arbitrarily small divisors, while, among zero-inclination (equatorial) orbits, geostationary ones are near optimal. The main ${\ensuremath{\alpha}}_{1}$-induced effects are (i) a complex secular evolution of the eccentricity vector of the orbit, describable as the vectorial sum of several independent rotations, and (ii) a yearly oscillation in the longitude of the satellite.